When I was living in Portland it was super common for people to bring their own mugs (usually those metal camping style cups with closable tops, but I'd see plastic cups too) to coffee shops. The baristas would usually blast them with some steam to clean them out then fill 'em up! Easy as pie.

This is my preference. My coffee cup keeps my drink hot way longer than any disposable one can and I would save a dime. Win, win, from my view.